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<div class="title">Bisection.hpp</div>  </div>
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<a href="_bisection_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#pragma once</span></div><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;</div><div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="_types_8hpp.html">NumCpp/Core/Types.hpp</a>&quot;</span></div><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="_iteration_8hpp.html">NumCpp/Roots/Iteration.hpp</a>&quot;</span></div><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;</div><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="preprocessor">#include &lt;cmath&gt;</span></div><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="preprocessor">#include &lt;functional&gt;</span></div><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="preprocessor">#include &lt;utility&gt;</span></div><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;</div><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespacenc.html">nc</a></div><div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;{</div><div class="line"><a name="l00044"></a><span class="lineno"><a class="line" href="namespacenc_1_1roots.html">   44</a></span>&#160;    <span class="keyword">namespace </span>roots</div><div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    {</div><div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        <span class="comment">//================================================================================</span></div><div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;        <span class="comment">// Class Description:</span></div><div class="line"><a name="l00050"></a><span class="lineno"><a class="line" href="classnc_1_1roots_1_1_bisection.html">   50</a></span>&#160;<span class="comment"></span>        <span class="keyword">class </span><a class="code" href="classnc_1_1roots_1_1_bisection.html">Bisection</a> : <span class="keyword">public</span> <a class="code" href="classnc_1_1roots_1_1_iteration.html">Iteration</a></div><div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;        {</div><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;        <span class="keyword">public</span>:</div><div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;            <span class="comment">//============================================================================</span></div><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;            <span class="comment">// Method Description:</span></div><div class="line"><a name="l00060"></a><span class="lineno"><a class="line" href="classnc_1_1roots_1_1_bisection.html#a5a790e250fbf36fd99584f68099e315b">   60</a></span>&#160;<span class="comment"></span>            <a class="code" href="classnc_1_1roots_1_1_bisection.html#a5a790e250fbf36fd99584f68099e315b">Bisection</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> epsilon, </div><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;                <span class="keyword">const</span> std::function&lt;<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)&gt;&amp; <a class="code" href="namespacenc_1_1random.html#aabf17da1f94e6da4ec99085feca10799">f</a>) noexcept :</div><div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;                <a class="code" href="classnc_1_1roots_1_1_iteration.html#a2d7285a81c033d56ce8283b6dbfca136">Iteration</a>(epsilon),</div><div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;                f_(<a class="code" href="namespacenc_1_1random.html#aabf17da1f94e6da4ec99085feca10799">f</a>)</div><div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;            {}</div><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;</div><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;            <span class="comment">//============================================================================</span></div><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;            <span class="comment">// Method Description:</span></div><div class="line"><a name="l00074"></a><span class="lineno"><a class="line" href="classnc_1_1roots_1_1_bisection.html#a0cac4b816910c90be235b0ad9487a2a4">   74</a></span>&#160;<span class="comment"></span>            <a class="code" href="classnc_1_1roots_1_1_bisection.html#a0cac4b816910c90be235b0ad9487a2a4">Bisection</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> epsilon, </div><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;                <span class="keyword">const</span> <a class="code" href="namespacenc.html#aacba4d66f94f6f53637e23c5d82e20d8">uint32</a> maxNumIterations,</div><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;                <span class="keyword">const</span> std::function&lt;<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)&gt;&amp; <a class="code" href="namespacenc_1_1random.html#aabf17da1f94e6da4ec99085feca10799">f</a>) noexcept :</div><div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;                <a class="code" href="classnc_1_1roots_1_1_iteration.html#a2d7285a81c033d56ce8283b6dbfca136">Iteration</a>(epsilon, maxNumIterations),</div><div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;                f_(<a class="code" href="namespacenc_1_1random.html#aabf17da1f94e6da4ec99085feca10799">f</a>)</div><div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;            {}</div><div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;</div><div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;            <span class="comment">//============================================================================</span></div><div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;            <span class="comment">// Method Description:</span></div><div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="comment"></span>            <a class="code" href="classnc_1_1roots_1_1_bisection.html#a6771fa331d511fa8a939ed0b2ba416c0">~Bisection</a>() noexcept override = default;</div><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;</div><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;            <span class="comment">//============================================================================</span></div><div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;            <span class="comment">// Method Description:</span></div><div class="line"><a name="l00095"></a><span class="lineno"><a class="line" href="classnc_1_1roots_1_1_bisection.html#a1199a68b6f57fee8b24bfc59ffeff486">   95</a></span>&#160;<span class="comment"></span>            <span class="keywordtype">double</span> <a class="code" href="classnc_1_1roots_1_1_bisection.html#a1199a68b6f57fee8b24bfc59ffeff486">solve</a>(<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b)</div><div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;            {</div><div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;                <a class="code" href="classnc_1_1roots_1_1_iteration.html#a85e79a4794bc3a6ac6bc3564956737a2">resetNumberOfIterations</a>();</div><div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;                checkAndFixAlgorithmCriteria(a, b);</div><div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;</div><div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;                <span class="keywordtype">double</span> x = 0.5 * (a + b);</div><div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;                <span class="keywordtype">double</span> fx = f_(x);</div><div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;</div><div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;                <span class="keywordflow">while</span> (std::fabs(fx) &gt;= <a class="code" href="classnc_1_1roots_1_1_iteration.html#a5eafe219bb90f82da4ece84f012a411a">epsilon_</a>)</div><div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;                {</div><div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                    x = calculateX(x, a, b, fx);</div><div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;                    fx = f_(x);</div><div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;</div><div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                    <a class="code" href="classnc_1_1roots_1_1_iteration.html#ae0ee7814d1fac03c4c91947f839ea401">incrementNumberOfIterations</a>();</div><div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;                }</div><div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;</div><div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;                <span class="keywordflow">return</span> x;</div><div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;            }</div><div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;</div><div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        <span class="keyword">private</span>:</div><div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;            <span class="comment">//============================================================================</span></div><div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;            <span class="keyword">const</span> std::function&lt;double(double)&gt; f_;</div><div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;</div><div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;            <span class="comment">//============================================================================</span></div><div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;            <span class="comment">// Method Description:</span></div><div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="comment"></span>            <span class="keywordtype">void</span> checkAndFixAlgorithmCriteria(<span class="keywordtype">double</span> &amp;a, <span class="keywordtype">double</span> &amp;b) <span class="keyword">const</span> noexcept</div><div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;            {</div><div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;                <span class="comment">//Algorithm works in range [a,b] if criteria f(a)*f(b) &lt; 0 and f(a) &gt; f(b) is fulfilled</span></div><div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;                <span class="keywordflow">if</span> (f_(a) &lt; f_(b))</div><div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;                {</div><div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                    <a class="code" href="namespacenc.html#a39da0502565b913855379ea1439047e1">std::swap</a>(a, b);</div><div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;                }</div><div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;            }</div><div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;</div><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;            <span class="comment">//============================================================================</span></div><div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;            <span class="comment">// Method Description:</span></div><div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="comment"></span>            <span class="keywordtype">double</span> calculateX(<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> &amp;a, <span class="keywordtype">double</span> &amp;b, <span class="keywordtype">double</span> fx) noexcept</div><div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;            {</div><div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;                <span class="keywordflow">if</span> (fx &lt; 0)</div><div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;                {</div><div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;                    b = x;</div><div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;                }</div><div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;                <span class="keywordflow">else</span></div><div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;                {</div><div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;                    a = x;</div><div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;                }</div><div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;</div><div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;                <span class="keywordflow">return</span> 0.5 * (a + b);</div><div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;            }</div><div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;        };</div><div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;    }</div><div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;}</div><div class="ttc" id="classnc_1_1roots_1_1_bisection_html_a6771fa331d511fa8a939ed0b2ba416c0"><div class="ttname"><a href="classnc_1_1roots_1_1_bisection.html#a6771fa331d511fa8a939ed0b2ba416c0">nc::roots::Bisection::~Bisection</a></div><div class="ttdeci">~Bisection() noexcept override=default</div></div>
<div class="ttc" id="namespacenc_html"><div class="ttname"><a href="namespacenc.html">nc</a></div><div class="ttdef"><b>Definition:</b> Coordinate.hpp:45</div></div>
<div class="ttc" id="namespacenc_html_aacba4d66f94f6f53637e23c5d82e20d8"><div class="ttname"><a href="namespacenc.html#aacba4d66f94f6f53637e23c5d82e20d8">nc::uint32</a></div><div class="ttdeci">uint32_t uint32</div><div class="ttdef"><b>Definition:</b> Types.hpp:41</div></div>
<div class="ttc" id="_iteration_8hpp_html"><div class="ttname"><a href="_iteration_8hpp.html">Iteration.hpp</a></div></div>
<div class="ttc" id="classnc_1_1roots_1_1_iteration_html_a85e79a4794bc3a6ac6bc3564956737a2"><div class="ttname"><a href="classnc_1_1roots_1_1_iteration.html#a85e79a4794bc3a6ac6bc3564956737a2">nc::roots::Iteration::resetNumberOfIterations</a></div><div class="ttdeci">void resetNumberOfIterations() noexcept</div><div class="ttdef"><b>Definition:</b> Iteration.hpp:94</div></div>
<div class="ttc" id="classnc_1_1roots_1_1_bisection_html_a5a790e250fbf36fd99584f68099e315b"><div class="ttname"><a href="classnc_1_1roots_1_1_bisection.html#a5a790e250fbf36fd99584f68099e315b">nc::roots::Bisection::Bisection</a></div><div class="ttdeci">Bisection(const double epsilon, const std::function&lt; double(double)&gt; &amp;f) noexcept</div><div class="ttdef"><b>Definition:</b> Bisection.hpp:60</div></div>
<div class="ttc" id="classnc_1_1roots_1_1_iteration_html_ae0ee7814d1fac03c4c91947f839ea401"><div class="ttname"><a href="classnc_1_1roots_1_1_iteration.html#ae0ee7814d1fac03c4c91947f839ea401">nc::roots::Iteration::incrementNumberOfIterations</a></div><div class="ttdeci">void incrementNumberOfIterations() noexcept</div><div class="ttdef"><b>Definition:</b> Iteration.hpp:105</div></div>
<div class="ttc" id="classnc_1_1roots_1_1_iteration_html"><div class="ttname"><a href="classnc_1_1roots_1_1_iteration.html">nc::roots::Iteration</a></div><div class="ttdoc">ABC for iteration classes to derive from. </div><div class="ttdef"><b>Definition:</b> Iteration.hpp:47</div></div>
<div class="ttc" id="classnc_1_1roots_1_1_bisection_html_a1199a68b6f57fee8b24bfc59ffeff486"><div class="ttname"><a href="classnc_1_1roots_1_1_bisection.html#a1199a68b6f57fee8b24bfc59ffeff486">nc::roots::Bisection::solve</a></div><div class="ttdeci">double solve(double a, double b)</div><div class="ttdef"><b>Definition:</b> Bisection.hpp:95</div></div>
<div class="ttc" id="_types_8hpp_html"><div class="ttname"><a href="_types_8hpp.html">Types.hpp</a></div></div>
<div class="ttc" id="namespacenc_1_1random_html_aabf17da1f94e6da4ec99085feca10799"><div class="ttname"><a href="namespacenc_1_1random.html#aabf17da1f94e6da4ec99085feca10799">nc::random::f</a></div><div class="ttdeci">NdArray&lt; dtype &gt; f(const Shape &amp;inShape, dtype inDofN, dtype inDofD)</div><div class="ttdef"><b>Definition:</b> f.hpp:59</div></div>
<div class="ttc" id="classnc_1_1roots_1_1_iteration_html_a5eafe219bb90f82da4ece84f012a411a"><div class="ttname"><a href="classnc_1_1roots_1_1_iteration.html#a5eafe219bb90f82da4ece84f012a411a">nc::roots::Iteration::epsilon_</a></div><div class="ttdeci">const double epsilon_</div><div class="ttdef"><b>Definition:</b> Iteration.hpp:115</div></div>
<div class="ttc" id="namespacenc_html_a39da0502565b913855379ea1439047e1"><div class="ttname"><a href="namespacenc.html#a39da0502565b913855379ea1439047e1">nc::swap</a></div><div class="ttdeci">void swap(NdArray&lt; dtype &gt; &amp;inArray1, NdArray&lt; dtype &gt; &amp;inArray2) noexcept</div><div class="ttdef"><b>Definition:</b> swap.hpp:43</div></div>
<div class="ttc" id="classnc_1_1roots_1_1_iteration_html_a2d7285a81c033d56ce8283b6dbfca136"><div class="ttname"><a href="classnc_1_1roots_1_1_iteration.html#a2d7285a81c033d56ce8283b6dbfca136">nc::roots::Iteration::Iteration</a></div><div class="ttdeci">Iteration(double epsilon) noexcept</div><div class="ttdef"><b>Definition:</b> Iteration.hpp:56</div></div>
<div class="ttc" id="classnc_1_1roots_1_1_bisection_html"><div class="ttname"><a href="classnc_1_1roots_1_1_bisection.html">nc::roots::Bisection</a></div><div class="ttdef"><b>Definition:</b> Bisection.hpp:50</div></div>
<div class="ttc" id="classnc_1_1roots_1_1_bisection_html_a0cac4b816910c90be235b0ad9487a2a4"><div class="ttname"><a href="classnc_1_1roots_1_1_bisection.html#a0cac4b816910c90be235b0ad9487a2a4">nc::roots::Bisection::Bisection</a></div><div class="ttdeci">Bisection(const double epsilon, const uint32 maxNumIterations, const std::function&lt; double(double)&gt; &amp;f) noexcept</div><div class="ttdef"><b>Definition:</b> Bisection.hpp:74</div></div>
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